Stability and convergence of semi-implicit time-stepping algorithm for stationary incompressible magnetohydrodynamics

2019 ◽  
Vol 77 (5) ◽  
pp. 1376-1395
Author(s):  
Jinjin Yang ◽  
Yinnian He
Keyword(s):  
Stability And Convergence ◽  
Implicit Time ◽  
Time Stepping ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Incompressible Magnetohydrodynamics

The Oseen Type Finite Element Iterative Method for the Stationary Incompressible Magnetohydrodynamics

2017 ◽  
Vol 9 (4) ◽  
pp. 775-794 ◽  
Author(s):  
Xiaojing Dong ◽  
Yinnian He
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Iterative Method ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Stability And Convergence ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Image Position ◽  
Incompressible Magnetohydrodynamics

AbstractIn this article, by applying the Stokes projection and an orthogonal projection with respect to curl and div operators, some new error estimates of finite element method (FEM) for the stationary incompressible magnetohydrodynamics (MHD) are obtained. To our knowledge, it is the first time to establish the error bounds which are explicitly dependent on the Reynolds numbers, coupling number and mesh size. On the other hand, The uniform stability and convergence of an Oseen type finite element iterative method for MHD with respect to high hydrodynamic Reynolds number Re and magnetic Reynolds number Rm, or small δ=1–σ with(C0, C1 are constants depending only on Ω and F is related to the source terms of equations) are analyzed under the condition that . Finally, some numerical tests are presented to demonstrate the effectiveness of this algorithm.

A Numerical Model of In-Channel Pebble Bed Thermal Storage for a Solar Chimney

2012 ◽  
Author(s):  
Brandon Schulte ◽  
O. A. Plumb
Keyword(s):  
Numerical Model ◽  
Present Model ◽  
Thermal Storage ◽  
Implicit Time ◽  
Heat Transfer Characteristics ◽  
Solar Chimney ◽  
Pebble Bed ◽  
One Dimensional ◽  
Time Stepping ◽  
Daily Energy

In this study, solar chimney performance is numerically modeled. Previously published models have considered water bags and natural earth as means to store daytime thermal energy for nighttime operation of the system. The present model considers in-channel pebble bed thermal storage. A one-dimensional, implicit time stepping numerical model is developed to predict solar chimney performance throughout a 24 hour period. The model is partially verified with available experimental data. The daily energy, daily efficiency and heat transfer characteristics of the solar chimney with pebble bed thermal storage are summarized. The numerical simulation showed that by introducing a pebble bed, nightly exit velocities reach 40% of the peak daytime velocity. However, the daily kinetic energy delivered by a solar chimney with pebble bed thermal storage is much less than a traditional solar chimney, suggesting pebble bed thermal storage is more practicable in building heating applications as opposed to power generation.

scholarly journals FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS

2019 ◽  
Vol 12 (2) ◽  
pp. 651-676 ◽  
Author(s):  
Christian Kühnlein ◽  
Willem Deconinck ◽  
Rupert Klein ◽  
Sylvie Malardel ◽  
Zbigniew P. Piotrowski ◽  
...  
Keyword(s):  
Finite Volume ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Implicit Time ◽  
Integration Scheme ◽  
Advective Transport ◽  
Numerical Weather ◽  
Time Stepping ◽  
Spectral Transform ◽  
Volume Integration

Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

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